Joint AVO inversion, wavelet estimation and noise‐level estimation using a spatially coupled hierarchical Bayesian model

The main objective of the AVO inversion is to obtain posterior distributions for P‐wave velocity, S‐wave velocity and density from specified prior distributions, seismic data and well‐log data. The inversion problem also involves estimation of a seismic wavelet and the seismic‐noise level. The noise model is represented by a zero mean Gaussian distribution specified by a covariance matrix. A method for joint AVO inversion, wavelet estimation and estimation of the noise level is developed in a Bayesian framework. The stochastic model includes uncertainty of both the elastic parameters, the wavelet, and the seismic and well‐log data. The posterior distribution is explored by Markov‐chain Monte‐Carlo simulation using the Gibbs' sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The use of a coloured seismic‐noise model resulted in about 10% lower uncertainties for the P‐wave velocity, S‐wave velocity and density compared with a white‐noise model. The uncertainty of the estimated wavelet is low. In the Heidrun example, the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results.

[1]  Anja Vogler,et al.  An Introduction to Multivariate Statistical Analysis , 2004 .

[2]  Arild Buland,et al.  Bayesian wavelet estimation from seismic and well data , 2003 .

[3]  Arild Buland,et al.  Rapid spatially coupled AVO inversion in the Fourier domain , 2003 .

[4]  A. Buland,et al.  Bayesian linearized AVO inversion , 2003 .

[5]  Arild Buland,et al.  The impact of common-offset migration on porosity estimation by AVO inversion , 2001 .

[6]  W. Michael Conklin,et al.  Monte Carlo Methods in Bayesian Computation , 2001, Technometrics.

[7]  Luis Tenorio,et al.  Prior information and uncertainty in inverse problems , 2001 .

[8]  Tadeusz J. Ulrych,et al.  A Bayes tour of inversion: A tutorial , 2001 .

[9]  R. White,et al.  Seismic amplitude inversion for interface geometry: practical approach for application , 2000 .

[10]  Alberto Malinverno,et al.  A Bayesian criterion for simplicity in inverse problem parametrization , 2000 .

[11]  Yanghua Wang.  Simultaneous inversion for model geometry and elastic parameters , 1999 .

[12]  J. Scales,et al.  Bayesian seismic waveform inversion: Parameter estimation and uncertainty analysis , 1998 .

[13]  Michael I. Jordan.  Graphical Models , 1998 .

[14]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[15]  David J. Spiegelhalter,et al.  Hepatitis B: a case study in MCMC methods , 1996 .

[16]  A. Buland,et al.  AVO Inversion of Troll Field Data , 1995 .

[17]  C. Robert.  The Bayesian choice , 1994 .

[18]  Henning Omre,et al.  Simulation of Random Functions on Large Lattices , 1993 .

[19]  George Christakos,et al.  Random Field Models in Earth Sciences , 1992 .

[20]  A. Duijndam.  BAYESIAN ESTIMATION IN SEISMIC INVERSION. PART I: PRINCIPLES1 , 1988 .

[21]  A. Duijndam.  BAYESIAN ESTIMATION IN SEISMIC INVERSION. PART II: UNCERTAINTY ANALYSIS1 , 1988 .

[22]  G. C. Smith,et al.  Weighted stacking for rock property estimation and detection of gas , 1987 .

[23]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  A. Tarantola,et al.  Inverse problems = Quest for information , 1982 .